In this work, we conduct a comparative study among the combine Laplace transform and modied Adomian decomposition method (LMADM) and two traditional methods for an analytic and approximate treatment of special type of nonlinear Volterra integro-differential equations of the second kind. The nonlinear part of integro-differential is approximated by Adomian polynomials, and the equation is reduce...

*Correspondence: [email protected] 1Department of Mathematical Sciences, University of Karachi, Karachi, 75270, Pakistan Full list of author information is available at the end of the article Abstract The aim of this article is to introduce the Laplace-Adomian-Padé method (LAPM) to the Riccati differential equation of fractional order. This method presents accurate and reliable results and has ...

Large classes of linear and nonlinear differential equations, both ordinary as well as partial, can be solved by the Adomian decomposition method [3, 4, 6]. This method is much more simpler in computation and quicker in convergence than any other method available in the open literature. The application of the fractional differential equation in physical problems is available in the book of Brac...

Adomian decomposition method has been applied to solve many functional equations so far. In this work, this method is applied to solve hyperbolic partial differential equations and results will be compared with characteristics method. 2004 Elsevier Inc. All rights reserved.

In this paper, the Combined Laplace Transform-Adomian Decomposition Method is used to solve nth-order integro-differential equations. The results show that the method is very simple and effective.

Keywords: Adomian decomposition method Padé approximants Belov–Chaltikian lattice The nonlinear self-dual network equations Solitary solution a b s t r a c t ADM-Padé technique is a combination of Adomian decomposition method (ADM) and Padé approximants. We solve two nonlinear lattice equations using the technique which gives the approximate solution with higher accuracy and faster convergence ...

In this work we will discuss the solution of an initial value problem of parabolic type. The main objective is to propose an alternative method of solution, one not based on finite difference or finite element or spectral methods. The aim of the present paper is to investigate the application of the Adomian decomposition method for solving the Fokker–Planck equation and some similar equations. ...

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I discuss a recent application of homotopy perturbation and Adomian decomposition methods to the linear and nonlinear Schrödinger equations. I propose a generalization of the procedure for the treatment of a wider class of problems.